I have two Nvidia 470s that I run three monitors off of. While playing a game, it makes my office rather hot. Is there a newer video card (s) that run cooler, will run three monitors and performs better than 2 470s in SLI??

depends on what you mean by run cooler, the GPU runs cooler or the ability to cool it better? MY 6950 does not exceed 70C, nor does my CPU exceed 35C, and I'm not aware of excess heat being expelled from the case.
Any high powered graphics card is going to produce a fair amount of heat, the only way round that is to get a less powered GPU, less watts = less heat, but I guess that won't provide the eye candy you are used to.
However, I would guess too that part of the heat is likely your PSU, powering 2 x 215w GPUs and an i7 is going to be putting a high load on a 750W PSU.
I would say either get a single awesome graphics card or a high wattage more efficent PSU would solve some heat issues.

Maybe sound silly but I have found best way to reduce some temperatures is to focus not just on fan and case but ambient room temperature! develop fan, cool window air or air condition in the room, and watch temperature in computer fall dramatic!

Maybe sound silly but I have found best way to reduce some temperatures is to focus not just on fan and case but ambient room temperature! develop fan, cool window air or air condition in the room, and watch temperature in computer fall dramatic!

He doesn't make much sense but does have a bit of a point many seem to overlook. Not long ago it was really cold in my area and I had all of the windows open. My idle CPU temps dropped from 35C to 26C, without doing a thing. It does seem to have a pretty large impact. That being said, if your case, cooler and fan situation is garbage, I don't think ambient room temperature is going to help you lol